Intersection Multiplicity, Canonical Element & Related Problems in Algebra

该奖项支持交换代数中两组主要问题的工作。 主要研究者将致力于塞尔猜想的interesection多重模块和周群的一个完整的分歧定期局部环。 他还将致力于规范元素猜想的霍希斯特和相关问题。 本研究涉及交换代数和代数几何中的一些问题。 代数几何研究多项式方程族的解。 人们既可以研究解集的几何，也可以通过研究形成交换环的解集上的某些函数来代数地处理问题。 这种双重视角在交换代数和代数几何之间建立了密切的联系。

This award supports work on two sets of major problems in commutative algebra. The principal investigator will work on Serre's conjecture on interesection multiplicity of modules and Chow groups of a complete ramified regular local ring. He will also work on the canonical element conjecture of Hochster and related problems. This research is concerned with a number of questions in commutative algebra and algebraic geometry. Algebraic geometry studies solutions of families of polynomial equations. One can either study the geometry of the solution set or approach problems algebraically by investigating certain functions on the solution set that form what is called a commutative ring. This dual perspective creates a close connection between commutative algebra and algebraic geometry.